PRL 94, 063401 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending18 FEBRUARY 2005

Observation of Cold, Long-Lived Antiprotonic Helium Ions

M. Hori,1 J. Eades,2 R. S. Hayano,2 W. Pirkl,2 E. Widmann,2 H. Yamaguchi,2 H. A. Torii,3 B. Juhasz,4 D. Horvath,5

K. Suzuki,6 and T. Yamazaki71CERN, CH-1211 Geneva 23, Switzerland

2Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan3Institute of Physics, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan

4Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, Hungary5KFKI Research Institute for Particle and Nuclear Physics, H-1525 Budapest, Hungary

6Physik-Department, Technische Universitat Munchen, D-85747 Garching, Germany7Heavy Ion Nuclear Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan

(Received 31 July 2004; published 14 February 2005)

0031-9007=

Cold, two-body antiprotonic helium ions p 4He2� and p 3He2� with 100-ns-scale lifetimes, occupyingcircular states with the quantum numbers ni � 28–32 and ‘i � ni � 1 have been observed. They wereproduced by cooling three-body antiprotonic helium atoms in an ultra-low-density helium target attemperature T � 10 K by atomic collisions, and then removing their electrons by inducing a lasertransition to an autoionizing state. The lifetimes of p 3He2� against annihilation induced by collisionswere shorter than those of p 4He2�, and decreased for larger-ni states.

DOI: 10.1103/PhysRevLett.94.063401 PACS numbers: 36.10.–k, 25.43.+t, 34.90.+q

4He+

4He2+

p–

p–

n=31

32

33

34

3535

36

37

264.7

372.6

470.7

713.6

597.3

672.8

28

29

30

31

ni = 32

l=27 28 29 30 31 32 33 34 35

metastable

3He+

3He2+

p–

p–

short-lived

n=31

32

33

34

35

36

3738

287.4

364.4

463.9

593.4

28

29

30

ni = 31

FIG. 1. Portion of energy level diagram of pHe2� ions andpHe� atoms. Wavelengths of the laser transitions are indicatedin nanometers The curved arrows indicate Auger transitions toionic states, and the straight arrows radiative pHe2� transitions.

The antiprotonic helium ion (pHe2�) [1,2] is a singlycharged, two-body Coulomb system composed of an anti-proton and a helium nucleus. We here report on the firstproduction of cold ions of the p 4He2� and p 3He2� iso-topes with lifetimes (�i � 100 ns) against annihilation.These highly excited circular states, which had principaland angular momentum quantum numbers ni � 28–32 and‘i � ni � 1, were selectively populated by cooling three-body antiprotonic helium atoms by atomic collisions, andthen removing their electrons by inducing a laser transitionto an autoionizing state.

These ions constitute ideal semiclassical Bohr systemswhose spin-independent parts of the energy levels (left sideof Fig. 1) can be theoretically calculated to very highprecision (�10�8) using the simple equation [3]

En � �4R1hc

n2i

Mme

Q2p

e2 ; (1)

where the reduced mass of the system is denoted by M, theelectron mass by me, the Rydberg constant by R1, and theantiproton and electron charges by Qp and e. For compari-son, in the 2p state of atomic hydrogen relativistic correc-tions to the above equation appear at a level of �10�5 andQED corrections at �10�6 [3]. These effects are very smallin the pHe2� case, partly because of the large mass andsmall magnetic moment of the antiproton, and partly be-cause the probability density of its semiclassical orbits arecircular and have almost no overlap with the helium nu-cleus. A single isolated ion can easily be shown to havetypical lifetimes near ni � 30 of �i � 0:3–0:4 �s againstannihilation, as the antiproton undergoes a series of radia-tive transitions [3] of the type �ni � �‘i � �1 (indicated

05=94(6)=063401(4)$23.00 063401-1 2005 The American Physical Society

0

2

4

6

8

2.1 2.2 2.3 2.4 2.5

(a):2x1018 cm-3

2.6 2.7 2.8 2.9 3

(b):3x1016 cm-3

Sig

nal

(a.

u.)

Elapsed time (µs)

FIG. 2. Annihilation spike produced by inducing the p 4He�

transition �n; ‘� � �39; 35� ! �38; 34�, measured at a high targetdensity (a). A prolongation of the tail is observed at ultralowdensities (b), indicating the formation of long-lived p 4He2� ionspopulating state �ni; ‘i� � �32; 31�.

PRL 94, 063401 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending18 FEBRUARY 2005

with straight arrows in Fig. 1), before being absorbed bythe nucleus from the ni � 3 region [4].

The antiproton mass and charge were recently deter-mined to a precision of one part in 108 by combining theresults of laser spectroscopy experiments [5] on the neutralthree-body pHe� � p� He2� � e� atom [6], and thecyclotron frequency of antiprotons measured in aPenning trap [7]. These derivations, however, relied heav-ily on the results of difficult three-body QED calculationsof the pHe� atomic energy levels (right side of Fig. 1)which currently have errors (�10�8) similar in magnitudeto those of the measured laser transition frequencies [8,9].This is not the case for the two-body pHe2�, where thelong lifetime necessary for laser spectroscopy is coupledwith extreme ease in calculating its energy levels; thesefactors may make this ion a better candidate than the pHe�

atom for determining the properties of antiprotons at thehighest precision.

Antiprotons coming to rest in helium can producepHe2� ions in doubly ionizing collisions with heliumatoms when their kinetic energy falls to E� 10 eV[10,11]. The produced ions recoil with kinetic energycorresponding to temperature T � 104 K [10,11] andmust come to thermal equilibrium via numerous collisionswith the surrounding gas (e.g., at �10 K) if they are to bestudied by high precision laser spectroscopy. Only a fewsuch binary encounters, however, suffice for collisionalStark effects to mix the high-‘i states with the S, P, andD states [10–13], and since these have a large overlap withthe helium nucleus, the ion will be normally destroyedwithin picoseconds [4,12–15].

A two-step method that solves these problems and pro-duces cold, long-lived pHe2� ions occupying a given state�ni; ‘i� was suggested by the laser spectroscopy experi-ments with high-�n; ‘� neutral pHe� atoms referred toabove. These atoms reach thermal equilibrium intact andsurvive for several microseconds afterward because theelectron inhibits collisional Stark mixing [6]. This allowstransitions to Auger-dominated states �nA; ‘A� to be sub-sequently induced by a laser, and a spontaneous Augerdecay will then produce the nearest ionic state �ni; ‘i�:

pHe��n;‘�!

h�pHe�

�nA;‘A�! pHe2�

�ni;‘i�� e�: (2)

In these pHe� experiments, the Auger decay lifetime�A�nA;‘A� was visible as the tail of an annihilation rate‘‘spike’’ (Fig. 2) that appeared when the laser induced atransition to state �nA; ‘A�. Normally, collisional Starkmixing once again immediately destroys any ion producedsubsequently by the Auger process, in which case thelength of the tail measures �A

�nA;‘A�directly (folded with

the timing resolution of the laser pulse). In fact the Augerlifetime of most neutral pHe� states measured in this waydoes agree with theoretical values within the experimentalerrors [8,9,16]. We expected, however, that as the target

06340

density (i.e., collision rate) was reduced, the pHe2� ion’sown lifetime would begin to compete with the Auger life-time of its parent pHe� state. This would be seen as alengthening of the tail and should therefore be an unam-biguous signature of the production of cold, long-livedions. If we assume ions thermalized to temperature T tobe destroyed in binary collisions with helium atoms attarget density �, their decay rate will be

�i��� � �i�� � 0� � ��

�������������8kBT�Mred

s; (3)

where the cross section of collision-induced annihilation isdenoted by �, the Boltzmann constant by kB, and thereduced mass of the pHe2�-He system by Mred. Previousexperiments had revealed no such effect, but assuming across section of �� 10�15 cm�3, it seemed likely that thecollision rate at even the lowest helium densities usedheretofore [�� �0:5 � 1:5� 1018 cm�3 in Ref. [5]—it-self 103–104 times lower than in previous experiments [6] ]had been 1–2 orders of magnitude too high to produce it.

The experimental setup was similar to the one usedpreviously to study neutral pHe� atoms [5], but themuch lower target densities and higher time resolutionsneeded to unambiguously demonstrate the production ofpHe2� ions necessitated numerous modifications in theparticle decelerator, target, detectors, and laser systems.Beam pulses containing 3 107 antiprotons with energyE � 5:3 MeV, pulse length �t � 100 ns, and repetitionrate f � 0:01 Hz were produced by the antiproton decel-erator (AD) of CERN. A radio frequency quadrupole de-celerator (RFQD) [17] decelerated some �30% of theantiprotons in each pulse to energies T � 80 keV; thesewere diverted by an achromatic momentum analyzer con-sisting of dipole, quadrupole, and solenoidal magnets con-nected to the output of the RFQD, and entered a helium gastarget through a 1:3-�m-thick polyethylene naphthalatewindow. The target was a 15-cm-diameter, 30-cm-longcylindrical chamber filled with 4He (purity 99.9999%) or

1-2

0

100

200

0

100

200

0

100

200

(32,31) 672.8 nm (32,31) 713.6 nm

(32,31) 597.3 nm (31,30) 470.7 nm

(30,29) 372.6 nm (28,27) 264.7 nm

0

100

200

0

100

200

0 10 20

(31,30) 593.4 nm (30,29) 463.9 nm

(29,28) 364.4 nm (28,27) 287.4 nm

Density ( x1017 cm-3 )

Dec

ay r

ate

(µ

s-1)

0 10 20

FIG. 3. Decay rates of annihilation signals measured at varioustarget densities. Data corresponding to p 4He2� states are in-dicated by filled circles, and those of p 3He2� by triangles.

PRL 94, 063401 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending18 FEBRUARY 2005

3He (99.997%) gas at temperature T � 10 K. We managedto stop antiprotons and form pHe� within the volume ofthe chamber at helium density � � 3 1016 cm�3; thiswas made possible by minimizing the energy spread andemittance of the antiproton beam through careful tuning ofthe electron beam cooler of the AD [18], optimizing thetrajectory of the antiprotons through the RFQD usingmicrowire beam profile monitors, adjusting the outputenergy of the RFQD by biasing its electrodes with a highvoltage [17], and utilizing a target entrance window ofsuperior thickness uniformity (better than �100 nm) com-pared to those previously [5] used. The gas pressure (typi-cally p� 3 10�2 mb) was measured using capacitancemanometers. Charged pions emerging from antiproton an-nihilations were detected by Cherenkov counters surround-ing the target, equipped with a microchannel platephotomultiplier which measured the envelope of theCherenkov light with subnanosecond time resolution. Byrecording the waveform with a digital oscilloscope, de-layed annihilation time spectra (the distribution of thenumber of antiproton annihilations, as a function of timeelapsed since the neutral pHe� was formed) were re-corded. A Nd:YAG-pumped dye laser with four dye am-plification stages produced 2–4-ns-long laser pulses tunedto wavelengths � 264–726 nm with the high energyrequired here (" � 10–80 mJ=pulse). In order to irradiateall the antiprotons stopped in the target, the laser beam wasexpanded to a diameter d � 12 cm using 15-cm-diameterlenses and allowed to enter the target through two 12-cm-diameter fused silica windows.

The time spectra of Fig. 2 confirm the reasoning outlinedabove concerning the tails of spikes in the annihilationdistributions. Figure 2(a) was found at the high targetdensity � � 2 1018 cm�3 by tuning the laser to thewavelength � 597:3 nm of a p4He� transition fromstate �n; ‘� � �39; 35� with lifetime ��39;35� � 1:4 �s, to astate �n; ‘� � �38; 34� with a short Auger lifetime �A

�38;34� �

9 ns [8,9,16]. Auger emission (curved arrow in Fig. 1) thenproduced the pHe2� ionic state �ni; ‘i� � �32; 31�. Theannihilation spike decayed with lifetime �obs��9�1� ns,which indicates that the ion was destroyed by collisions ina short time relative to the pHe� Auger lifetime �A

�38;34� �

9 ns. When the same transition was measured at a100 times lower density � � 3 1016 cm�3, however,the lifetime increased by an order of magnitude to �obs ��90 � 20� ns [Fig. 2(b)], due to the prolonged collisionallifetime �i of the ion occupying �ni; ‘i� � �32; 31�. Thisspectrum, representing data accumulated from �1010 anti-protons stopped in the target, includes �106 such ions. Thelaser was fired at time t > 2 �s after antiproton arrival, toallow the pHe� to thermalize to the gas temperature T �10 K. The temperature of the ions was inferred from theobserved thermal Doppler widths (� < 500 MHz) of the597.3-nm pHe� resonance; the pHe2� ions produced sub-sequently have roughly the same temperature, since the

06340

kinetic energy of the emitted Auger electron is verylow (EA�38;34� � 0:8 eV, corresponding to the energy differ-ence between the Auger-dominated pHe� and finalpHe2� states; see Fig. 1). This results in a �100-�eVrecoil energy for the ion.

Further support for the production of ions was providedby populating the same p 4He2� state �ni; ‘i� � �32; 31� bydriving two other p 4He� transitions: �n; ‘� � �40; 35� !�39; 34� at wavelength � 672:8 nm, and �37; 34� !�38; 33� at 713.6 nm. Despite the fact that the three tran-sitions involved intermediate states having very differentAuger [8,9,16] lifetimes (�9 ns, �1 ns, and �3 ps, re-spectively) and emission energies of the Auger electron(0.8 eV, 2.6 eV, and 0.5 eV, respectively), the observedlifetimes �obs of the tails of the corresponding annihilationspikes agreed with one another at low target densities � <6 1017 cm�3, where the ion’s lifetime is expected todominate (i.e., �obs � �i). This result is consistent withthe expectation that all three p 4He� transitions ultimatelyproceed to the same long-lived p 4He2� state �ni; ‘i� ��32; 31�.

We measured the lifetimes �i of p 4He2� produced attarget densities between � � 3 1016 and 2 1018 cm�3

initially occupying four states: �ni; ‘i� � �32; 31� (de-

1-3

0

1

2

3

4

28 29 30 31 32

Dec

ay r

ate

gra

die

nt

(10-1

6 MH

z cm

3 )

Ionic principal quantum number ni

FIG. 4. Gradients of the decay rates per target density of fourp 4He2� (indicated by filled circles) and p 3He2� (triangles)ionic states, as a function of the principal quantum number ni.

PRL 94, 063401 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending18 FEBRUARY 2005

scribed above), �31; 30� (populated by inducing the �470:7-nm transition, the intermediate pHe� state havingan Auger lifetime �5 ns), �30; 29� (372.6 nm, Auger life-time �5 ns), and �28; 27� (264.7 nm, reliable Auger life-time is unavailable). Four p 3He2� states �31; 30�, �30; 29�,�29; 28�, and �28; 27� were also measured using the p 3He�

transitions at � 593:4, 463.9, 364.4, and 287.4 nm, theAuger-dominated states of which had lifetimes of about 3,1, 1, and 4 ns, respectively. In Fig. 3, the observed decayrates �obs of the tails of the annihilation spikes are plottedas a function of target density, with the correspondingpHe2� ionic state and the wavelength of the pHe� tran-sition indicated in each case. It is interesting to note thatwhen compared at the same density (e.g., � �4 1017 cm�3), the collisional decay rates of p 3He2�

increase for larger ni values [�obs � 0:09�1�, 0.12(3),0.17(1), and 0:18�1� ns�1 for the ionic states �28; 27�,�29; 28�, �30; 29�, and �31; 30�, respectively].

In the region � < �5 � 10� 1017 cm�3, �obs increasedroughly as a linear function of density, as indicated by solidlines in Fig. 3. This qualitatively agrees with expectationsfor pHe2� ions destroyed in binary collisions with heliumatoms as described by Eq. (3). The weak transition at �713:6 nm could not be observed at densities � < 5 1017 cm�3, and so it is not analyzed here. Although areliable extrapolation of all these decay rates to � � 0was not possible due to the large systematic errors asso-ciated with measuring gas densities � < 3 1017 cm�3,the data are consistent with the theoretical expectation ofisolated ions having lifetimes of a few hundred nanosec-onds against annihilation. At high densities � > 1 1018 cm�3, the �obs values of four transitions at �597:3, 470.7, 372.6, and 287.4 nm saturated to valuesconsistent with the theoretical Auger values �A � 4–9 nsfolded with the time resolution �las � 4 ns of the laserpulse, as indicated by dotted lines in Fig. 3. The othertransitions involving shorter Auger lifetimes �A < 2 nssaturated to values corresponding to this resolution �las.

The measured gradients d�i=d� are plotted as a functionof the ni value in Fig. 4. The collisional decay rates ofp 3He2� were consistently larger than those of p 4He2�

06340

measured at the same target temperature and pressure; thisqualitatively agrees with the expectation of Eq. (3) thatp 3He2� � 3He collisions have higher quenching rates thanp 4He2� � 4He due to the smaller reduced mass Mred. Thed�i=d� value in p 3He2� increased from 1:9�3� 10�16 to3:2�3� 10�16 MHz cm3 for increasing ni from 28 to 31,whereas the ni dependence appears to be smaller inp4He2�, d�i=d� being distributed around �1 � 2� 10�16 MHz cm3.

The cross section of ions destroyed by collisions wasestimated from the measured decay rates and Eq. (3) as�� �4–10� 10�15 cm2. This value is an order of mag-nitude larger than theoretical cross sections [4,12,13] forcollisional Stark mixing, but as these theories pertain topHe2� recoiling at temperature T � 104 K, they cannot bedirectly compared with the present experiment carried outon cold ions. These results indicate that laser spectroscopyof pHe2� may be possible, by inducing transitions betweenionic states with different ni values and making use of theni dependence of their lifetimes to detect the resonancesignal.

We thank the CERN AB division, cryogenic laboratory,T. S. Jensen, R. Landua, and V. E. Markushin for their help.This work was supported by the Grant-in-Aid for SpeciallyPromoted Research (15002005) of Monbukagakusho ofJapan and by the Hungarian Scientific Research Fund(OTKA T046095 and TeT-Jap-4/00).

1-4

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